Page 229 - 48Fundamentals of Compressible Fluid Mechanics

11.4. RAPID EVACUATING OF A RIGID TANK 191
11.3.2 Isothermal Nozzle Attached

In this case the process in nozzle is assumed to isothermal but the process in the
chamber is isentropic. The temperature in the nozzle is changing because the
temperature in the chamber is changing. Yet, the differential temperature change
in the chamber is slower than the temperature change in nozzle. For rigid volume,
and for isothermal nozzle Thus, equation (11.13) is reduced into

(11.29)
>
>

Separating the variables and rearranging equation (11.30) converted into
>

>

>*

(11.30)

B
Here, is expressed by equation (11.22). After the integration, equation

(11.30) transformed into >

>

>*

(11.31)

>*

> %

*

B
11.4 Rapid evacuating of a rigid tank
> (
11.4.1 With Fanno Flow

, is constant and equal one for a completely rigid
tank. In such case, the general equation (11.17) “shrinks” and doesn’t contain the

relative volume term. >
The relative Volume, *
A reasonable model for the tank is isentropic (can be replaced polytropic
relationship) and Fanno flow are assumed for the flow in the tube. Thus, the specific
governing equation is
(11.32)
For a choked flow the entrance Mach number to the tube is at its maximum,

E
and therefore . The solution of equation (11.37) is obtained by noticing that
>
>
%
>
is not a function of time and by variables separation results in N

>*
?PO

>

(11.33)

>

B

>
>
>*

>
>
>

>